
theorem
  2633 is prime
proof
  now
    2633 = 2*1316 + 1; hence not 2 divides 2633 by NAT_4:9;
    2633 = 3*877 + 2; hence not 3 divides 2633 by NAT_4:9;
    2633 = 5*526 + 3; hence not 5 divides 2633 by NAT_4:9;
    2633 = 7*376 + 1; hence not 7 divides 2633 by NAT_4:9;
    2633 = 11*239 + 4; hence not 11 divides 2633 by NAT_4:9;
    2633 = 13*202 + 7; hence not 13 divides 2633 by NAT_4:9;
    2633 = 17*154 + 15; hence not 17 divides 2633 by NAT_4:9;
    2633 = 19*138 + 11; hence not 19 divides 2633 by NAT_4:9;
    2633 = 23*114 + 11; hence not 23 divides 2633 by NAT_4:9;
    2633 = 29*90 + 23; hence not 29 divides 2633 by NAT_4:9;
    2633 = 31*84 + 29; hence not 31 divides 2633 by NAT_4:9;
    2633 = 37*71 + 6; hence not 37 divides 2633 by NAT_4:9;
    2633 = 41*64 + 9; hence not 41 divides 2633 by NAT_4:9;
    2633 = 43*61 + 10; hence not 43 divides 2633 by NAT_4:9;
    2633 = 47*56 + 1; hence not 47 divides 2633 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2633 & n is prime
  holds not n divides 2633 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
